PCSY-D-24-00126

Urban scaling with missing data

PLOS Complex Systems

Dear Dr. Porfiri,

Thank you for submitting your manuscript to PLOS Complex Systems. After careful consideration, we feel that it has merit but does not fully meet PLOS Complex Systems's publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Please submit your revised manuscript within 60 days Nov 22 2024 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at complexsystems@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pcsy/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

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We look forward to receiving your revised manuscript.

Kind regards,

Haroldo V. Ribeiro

Academic Editor

PLOS Complex Systems

Haroldo Ribeiro

Academic Editor

PLOS Complex Systems

Journal Requirements:

Additional Editor Comments (if provided):

Your manuscript was reviewed by two experts who noted that it addresses a critical issue that is currently largely overlooked in urban scaling studies. However, they have provided several suggestions and comments that should be addressed in a revised version. One of the reports refers to published works in which I am a coauthor; please cite them only if you believe they will contribute meaningfully to your discussion and analysis.

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Does this manuscript meet PLOS Complex Systems’s publication criteria? Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe methodologically and ethically rigorous research with conclusions that are appropriately drawn based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

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2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

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3. Have the authors made all data underlying the findings in their manuscript fully available (please refer to the Data Availability Statement at the start of the manuscript PDF file)?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception. The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

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4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS Complex Systems does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

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5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: The manuscript 'Urban Scaling with Missing Data' by Maurizio Porfiri et al. addresses the important issue of missing values that often occur in scaling analyses. The authors provide a detailed discussion of how incomplete data can impact urban scaling exponents. To address this challenge, they introduce a Greedy algorithm that offers upper and lower bounds. The methodology is generally robust and thorough, and potentially useful. However, I have some suggestions and considerations that could further enhance the manuscript and strengthen its arguments. Please see my review in the attachment.

Reviewer #2: In this paper, the authors examine the impact of incomplete information on the estimation of urban scaling and propose a method to find the boundaries for the scaling exponent. They test their approach using real-world data. The idea of working with partial information is a valuable contribution. The topic is both interesting and timely, as it addresses a subject that is not extensively covered in the growing literature on urban scaling.

In general, the paper is well-written, though there are areas where the authors could expand on certain concepts and condense others (discussed in more detail below).

I have three main comments about the paper

1. The authors provide methods to estimate the minimum and maximum potential scaling coefficients when only the top-k observations are available, while the total sum S is known. However, my concern is whether these boundaries are truly meaningful. Could they be too rigid or reflect arbitrary decisions that maximize or minimize the scaling exponent? For example, Fig. 4 shows the data modification that leads to β^min and β^max. Aren't they too arbitrary and thus meaningless? The authors should discuss this. The authors should consider making the boundaries more probabilistic, to better represent the distribution of the boundaries.

1.a Related to this, in L241, the authors state: “Therefore, we cannot reject the hypothesis of superlinearity or linearity for these states. For the remaining states, β^max < 1, indicating a sublinear behavior of firearm recoveries with respect to city population.” Wouldn't it be necessary to account for confidence intervals here?

2. While the authors propose a greedy algorithm to find the boundaries of the scaling exponent, I feel that more discussion is needed regarding the monotonicity of the function or the convexity of the objective. The authors must explore and discuss these properties to substantiate their claim that the proposed method indeed finds the true boundaries.

3. I find the title of the paper a bit misleading. The core problem that the authors tackles is “Within a system of N cities, we address the case in which the researcher has only access to urban measurements in a subsystem of k < N cities, and the total count of the urban feature S across all N cities.” Given that the total count S is known, the authors seem to be addressing "partial data" rather than working with missing data in the usual sense. This distinction is also important because the terminology shifts throughout the paper, with references to "suppressed" and "incomplete" data. I would suggest the authors clarify their terminology to consistently reflect that they are working with partial but constrained data.

3.a Likewise, the title would be way more informative if it explicitly indicates that the paper focuses on finding the boundaries of the scaling exponents.

Other issues:

- Line 171: There’s a slight leap in logic at this point. The authors should provide a clearer explanation of how the stated approach directly addresses their problem. It would really help the reader. A suggestion would be to start by motivating the use of OLS, followed by the presentation of Eq. (1).

- Around Line 388, while the matrix notation is elegant, it may confuse readers since it's not used again in the paper. Given that Eq. 5 is more relevant, it would be clearer to introduce the standard OLS formula first at Line 388, making it easier to understand Eq. 5 at Line 423.

- The pseudocode should use more meaningful variable names to help readability. For example, L could be replaced to something more meaningful.

- In explaining how the greedy algorithm works, “To find the Y^uk entries that result in β_max (β_min), we iteratively increase the value of each entry by one, without surpassing Y_max,i, and seek the largest increase (decrease) of f_β”, the authors should provide a more detailed explanation to help the reader, as the current description is a bit vague and could confuse the reader.

-- It would be useful to clarify how the algorithm handles ties. Perhaps using a random loop to break ties?

- Between Lines 30 and 51, the discussion could be condensed, as it feels like it slightly digresses. Similarly, the section between Lines 67 and 93 on types of missing data might be too detailed for the purposes of this paper.

- Line 137: The phrase "it is approximately independent of the true scaling exponent" is unclear. Could the authors clarify what they mean here?

- It's a question of style, but I find the notation (R^k)^2 seems unnecessarily cluttered; perhaps R_k^2?

- Fig. 4: the authors should consider adding the subscripts min and max to the beta in the legend.

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Reviewer #1: No

Reviewer #2: No

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Attachments

Attachment

Submitted filename: PLOS Complex Systems Review.docx

Urban scaling with censored data

PCSY-D-24-00126R1

Dear Dr. Porfiri,

We are pleased to inform you that your manuscript 'Urban scaling with censored data' has been provisionally accepted for publication in PLOS Complex Systems.

As detailed below, both reviewers have acknowledged that your revised version has significantly enhanced the quality of your work. There is one stylistic suggestion regarding the representation of Table 2, which you may choose to address during the formatting stage of your manuscript.

Before your manuscript can be formally accepted you will need to complete some formatting changes, which you will receive in a follow-up email from a member of our team. 

Please note that your manuscript will not be scheduled for publication until you have made the required changes, so a swift response is appreciated.

IMPORTANT: The editorial review process is now complete. PLOS will only permit corrections to spelling, formatting or significant scientific errors from this point onwards. Requests for major changes, or any which affect the scientific understanding of your work, will cause delays to the publication date of your manuscript.

If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they'll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact complexsystems@plos.org.

Thank you again for supporting Open Access publishing; we are looking forward to publishing your work in PLOS Complex Systems.

Best regards,

Haroldo V. Ribeiro

Academic Editor

PLOS Complex Systems

Hocine Cherifi

Editor-in-Chief

PLOS Complex Systems

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Reviewer Comments (if any, and for reference):

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: All comments have been addressed

Reviewer #2: All comments have been addressed

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2. Does this manuscript meet PLOS Complex Systems's publication criteria? Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe methodologically and ethically rigorous research with conclusions that are appropriately drawn based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available (please refer to the Data Availability Statement at the start of the manuscript PDF file)?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception. The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS Complex Systems does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: Revised version: Urban Scaling with censored data

Reviewer comments:

In my previous review, I requested amendments to the manuscript in response to my comments before its publication in PLOS Complex Systems. Initially, I found the proposed methodology both useful and highly relevant to the current scaling literature. However, I highlighted several aspects that required further analysis, clarification, or discussion, particularly regarding numerical simulations, bias, statistical properties, and Greedy bounds.

In my second assessment of this work, I found that the authors have thoroughly addressed all my comments, significantly enhancing the clarity and rigor of the manuscript. I, therefore, have no objections and am pleased to recommend its publication in PLOS Complex Systems.

Reviewer #2: The authors have addressed my comments in detail, and I appreciate the effort put into this revision.

I have just one style suggestion for Table 2, which is a bit cumbersome to read due to its length. To improve readability, the authors might consider including only an excerpt of the table in the main text (i.e., a few states), with the full version in the supplementary material. Alternatively, a simple figure with horizontal bar plots (i.e., each bar is the min, max, CI intervals) could make the results way easier to understand. This is purely a style suggestion, and the authors are welcome to disregard it if they prefer.

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7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

Do you want your identity to be public for this peer review? If you choose “no”, your identity will remain anonymous but your review may still be made public.

For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

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